In this Note, we deal with one-dimensional backward stochastic differential equations (BSDEs) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z, but without explicit growth constraint. We prove, in this setting, an existence theorem for backward stochastic differential equations.
Dans cette Note, nous traitons l'équation différentielle stochastique rétrograde en une dimension, où le coéfficient est Lipschitzien à gauche en y (peut-être discontinu) et Lipschitzien en z, sans croissance contrainte explicite. Nous montrons, dans ce cas, un théorème d'existence de la solution pour équation différentielle stochastique rétrograde.
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@article{CRMATH_2006__342_9_685_0, author = {Jia, Guangyan}, title = {A generalized existence theorem of {BSDEs}}, journal = {Comptes Rendus. Math\'ematique}, pages = {685--688}, publisher = {Elsevier}, volume = {342}, number = {9}, year = {2006}, doi = {10.1016/j.crma.2006.02.020}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.02.020/} }
TY - JOUR AU - Jia, Guangyan TI - A generalized existence theorem of BSDEs JO - Comptes Rendus. Mathématique PY - 2006 SP - 685 EP - 688 VL - 342 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.02.020/ DO - 10.1016/j.crma.2006.02.020 LA - en ID - CRMATH_2006__342_9_685_0 ER -
Jia, Guangyan. A generalized existence theorem of BSDEs. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 685-688. doi : 10.1016/j.crma.2006.02.020. http://archive.numdam.org/articles/10.1016/j.crma.2006.02.020/
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